Home/Chain Registry/Block #6,784,900

Block #6,784,900

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 4/5/2026, 10:29:53 PM · Difficulty 10.9808 · 7,808 confirmations

TWN

Bi-Twin Chain

Interleaved pairs of primes that differ by 2, forming twin prime pairs at each level.

Block Header

Block Hash

f06a1feb0c77498f56ddd0f1f99cbad37bc928438335f384c9676cc25a559a2b

View on Chainz ↗

Height

#6,784,900

Difficulty

10.980838

Transactions

Size

191 B

Version

536870912

Bits

0afb1832

Nonce

254,396,507

Timestamp

4/5/2026, 10:29:53 PM

Confirmations

7,808

Merkle Root

47d411aca112ca31704126f34e17f514515f69697e2589a3403c145f24ae203a

Transactions (1)

Coinbase47d411aca112ca…3c145f24ae203a

1 in → 1 out8.1790 XPM101 B

AMrLYUQN…jwjifxiz

Prime Chain Origin

This is the prime chain origin stored in the block header. It is a composite number (not prime itself) — it equals the first prime in the chain multiplied by a primorial. The origin anchors the entire chain to this specific block.

2.100 × 10⁹⁴(95-digit number)

21005548962591248997…84029761772353303360

Discovered Prime Numbers

Lower: 2^k × origin − 1 | Upper: 2^k × origin + 1

These are the actual prime numbers discovered by this block, computed using the verified Primecoin formula. Each number has been independently confirmed to pass the Fermat primality test. Use the FactorDB links to verify any number independently.

Level 0 — Twin Prime Pair (origin ± 1)

origin − 1

2.100 × 10⁹⁴(95-digit number)

21005548962591248997…84029761772353303359

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

2.100 × 10⁹⁴(95-digit number)

21005548962591248997…84029761772353303361

Verify on FactorDB ↗Wolfram Alpha ↗

Difference: origin + 1 − origin − 1 = 2 (twin primes ✓)

Level 1 — Twin Prime Pair (2^1 × origin ± 1)

2^1 × origin − 1

4.201 × 10⁹⁴(95-digit number)

42011097925182497995…68059523544706606719

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

4.201 × 10⁹⁴(95-digit number)

42011097925182497995…68059523544706606721

Verify on FactorDB ↗Wolfram Alpha ↗

Difference: 2^1 × origin + 1 − 2^1 × origin − 1 = 2 (twin primes ✓)

Level 2 — Twin Prime Pair (2^2 × origin ± 1)

2^2 × origin − 1

8.402 × 10⁹⁴(95-digit number)

84022195850364995990…36119047089413213439

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

8.402 × 10⁹⁴(95-digit number)

84022195850364995990…36119047089413213441

Verify on FactorDB ↗Wolfram Alpha ↗

Difference: 2^2 × origin + 1 − 2^2 × origin − 1 = 2 (twin primes ✓)

Level 3 — Twin Prime Pair (2^3 × origin ± 1)

2^3 × origin − 1

1.680 × 10⁹⁵(96-digit number)

16804439170072999198…72238094178826426879

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

1.680 × 10⁹⁵(96-digit number)

16804439170072999198…72238094178826426881

Verify on FactorDB ↗Wolfram Alpha ↗

Difference: 2^3 × origin + 1 − 2^3 × origin − 1 = 2 (twin primes ✓)

Level 4 — Twin Prime Pair (2^4 × origin ± 1)

2^4 × origin − 1

3.360 × 10⁹⁵(96-digit number)

33608878340145998396…44476188357652853759

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

3.360 × 10⁹⁵(96-digit number)

33608878340145998396…44476188357652853761

Verify on FactorDB ↗Wolfram Alpha ↗

Difference: 2^4 × origin + 1 − 2^4 × origin − 1 = 2 (twin primes ✓)

What this block proved

The miner who found this block proved the existence of 10 consecutive prime numbers forming a Bi-Twin Chain. The prime chain origin — the large number shown above — anchors the chain and is divisible by a primorial (the product of small primes), cryptographically tying these prime numbers to this specific block.

View full Prime Chain Discovery page →

★★☆☆☆

Rarity

UncommonChain length 10

How Primecoin's Proof-of-Work Constructs These Primes

Primecoin stores a value called the prime chain origin in each block. The miner found a large integer such that when divided by a primorial (the product of small primes: 2 × 3 × 5 × 7 × …), the result is the first prime in the chain. The origin is deliberately divisible by this primorial — that divisibility is part of the proof.

Prime Chain Origin = First Prime × Primorial (2·3·5·7·11·…)

Source: Primecoin prime.cpp — CheckPrimeProofOfWork()

This is why the origin has many small prime factors — those factors are the primorial divisor. The chain then extends from the first prime using the TWN formula:

TWN: twin pairs (p, p+2) where p = origin/primorial − 1 and p+2 = origin/primorial + 1

Verify on a Primecoin Node

Anyone running a Primecoin node can independently verify this block using the following RPC commands. Run these from the primecoin-cli command line or via the debug console in the Primecoin wallet.

1. Get block hash by height

getblockhash 6784900

Returns the block hash for a given block height. Use this to confirm the hash shown above matches the chain.

2. Get full block data

getblock f06a1feb0c77498f56ddd0f1f99cbad37bc928438335f384c9676cc25a559a2b

Returns the full block header including difficulty, prime chain origin, prime chain type, transaction IDs, and all other fields shown on this page.

How to run these commands: To verify this data independently, open a terminal on your own Primecoin node and run primecoin-cli <command>. Alternatively, open the Primecoin-Qt wallet, go to Help → Debug Window → Console, and type the command directly. The node must be fully synced to this block height for the commands to return results.

Cross-reference on Chainz Explorer

Chainz is an independent Primecoin block explorer. Compare this block's data to verify accuracy.

View Block #6,784,900 on Chainz ↗